No timeline has been established for Lawson's recovery from the surgery. The team said in its statement (embedded below, via Andy Young of Time Warner Cable News) that Lawson could have continued to play through the re-aggravated injury, but that the team now believes it is in Lawson's best interest to have the surgery now.
In the immediate aftermath of the Bills making Lawson the No. 19 overall pick late last month, ESPN's Adam Schefter reported that Lawson would require a shoulder surgery, which would likely take place after the 2016 season - and which could require 4-6 months of recovery time. It's unclear if Lawson is having that precise procedure, with that timeline, but clearly the need for a procedure accelerated, despite the Bills downplaying the significance of the injury two-plus weeks ago.
With surgery Tues, Shaq Lawson appears headed to the PUP list to start camp and potentially the regular season. Should correct it long-term— Ian Rapoport (@RapSheet) May 16, 2016
We'll have more on this story if and when more information becomes available.